MIMO refers to the use of multiple transmit antennas and multiple receive antennas for the transmission of a signal in order to improve performance. A highly schematised block diagram of a MIMO system is shown in FIG. 1. The system comprises a transmitter 2 having multiple antennas 6(1) . . . 6(n) and a receiver 4 having multiple antennas 8(1) . . . 8(m). For example, the transmitter may be a base station and the receiver may be a mobile terminal of a cellular communication system. The transmitter 2 transmits a signal on each of its antennas 6, and the receiver 4 receives the signal on each of its antennas 8. To achieve good closed-loop performance, the transmitter may perform MIMO “precoding”, which needs channel information to determine the relative amplitude and phase with which to transmit the signal on each antenna.
To obtain the closed-loop capacity of a MIMO system, channel state information is required at the transmitter. In general, this information has to be fed back from the receiver 4. To reduce the amount of feedback overhead, a precoding matrix approach was proposed in D. Love and R. W. Heath, “Limited Feedback Precoding for Spatial Multiplexing Systems”, in Proc. IEEE Globecom 2003, pp. 1857-1861. The basic idea behind this approach is to quantize the MIMO channel using a codebook consisting of a set of pre-defined matrices. For each channel realization, the receiver finds the best (according to some performance criteria) precoding matrix from the codebook shared between the receiver and the transmitter, and then feeds only the index of this matrix to the transmitter.
In a closed-loop MIMO-OFDM system, information on the best precoding matrix is provided to the base station transmitter through a precoding matrix indicator (PMI) corresponding to the actual channel, which is reported by the UE per group of sub-bands, where a sub-band is a predefined frequency resource.
To reduce the amount of signalling overhead required for the feedback, different compression schemes have been proposed in conjunction with the precoding approach. These schemes rely on the correlation in time or frequency (for the case of MIMO-OFDM system) of the channel. In other words, compression exploits the fact that the sequence of the channel precoding matrices is correlated. Consider for example the case of a scheme based on differential encoding, where only the offset of the precoding matrix index is sent instead of the index itself. The offset is computed from the subset of precoding matrices that are highly correlated with the initial precoding matrix. The correlation can be based on different metrics, including inner product, distance metrics, or other metrics.
However, although such encoding schemes reduce signalling overhead, they are also prone to error. Particularly, differential encoding schemes are prone to propagation of error.